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Solution of Ambartsumian Delay Differential Equation with Conformable Derivative

Author

Listed:
  • Sayed M. Khaled

    (Department of Studies and Basic Sciences, Faculty of Community, University of Tabuk, Tabuk 71491, Saudi Arabia
    Department of Mathematics, Faculty of Sciences, Helwan University, Cairo 11795, Egypt)

  • Essam R. El-Zahar

    (Department of Mathematics, College of Sciences and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-kharj 11942, Saudi Arabia
    Department of Basic Engineering Science, Faculty of Engineering, Menofia University, Shebin El-Kom 32511, Egypt)

  • Abdelhalim Ebaid

    (Department of Studies and Basic Sciences, Faculty of Community, University of Tabuk, Tabuk 71491, Saudi Arabia)

Abstract

This paper addresses the modelling of Ambartsumian equation using the conformable derivative as an application of the theory of surface brightness in astronomy. The homotopy perturbationmethod is applied to solve this model, where the approximate solution is given in terms of the conformable derivative order and the exponential functions. The present solution reduces to the corresponding one in the relevant literature as a special case. Moreover, a rapid rate of convergence has been achieved for the obtained approximate solutions. Furthermore, the accuracy of the obtained numerical results is validated via calculating the residual against the impeded parameters. It is shown graphically that the obtained residual approaches zero in various cases, which proves the efficiency of the current analysis.

Suggested Citation

  • Sayed M. Khaled & Essam R. El-Zahar & Abdelhalim Ebaid, 2019. "Solution of Ambartsumian Delay Differential Equation with Conformable Derivative," Mathematics, MDPI, vol. 7(5), pages 1-10, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:425-:d:230630
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    Citations

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    Cited by:

    1. Aneefah H. S. Alenazy & Abdelhalim Ebaid & Ebrahem A. Algehyne & Hind K. Al-Jeaid, 2022. "Advanced Study on the Delay Differential Equation y ′( t ) = ay ( t ) + by ( ct )," Mathematics, MDPI, vol. 10(22), pages 1-13, November.
    2. Ebrahem A. Algehyne & Musaad S. Aldhabani & Mounirah Areshi & Essam R. El-Zahar & Abdelhalim Ebaid & Hind K. Al-Jeaid, 2023. "A Proposed Application of Fractional Calculus on Time Dilation in Special Theory of Relativity," Mathematics, MDPI, vol. 11(15), pages 1-11, July.
    3. Laila F. Seddek & Abdelhalim Ebaid & Essam R. El-Zahar & Mona D. Aljoufi, 2023. "Exact Solution of Non-Homogeneous Fractional Differential System Containing 2 n Periodic Terms under Physical Conditions," Mathematics, MDPI, vol. 11(15), pages 1-12, July.
    4. Weam Alharbi & Sergei Petrovskii, 2020. "Numerical Analysis for the Fractional Ambartsumian Equation via the Homotopy Herturbation Method," Mathematics, MDPI, vol. 8(12), pages 1-11, December.
    5. Abdulrahman B. Albidah & Nourah E. Kanaan & Abdelhalim Ebaid & Hind K. Al-Jeaid, 2023. "Exact and Numerical Analysis of the Pantograph Delay Differential Equation via the Homotopy Perturbation Method," Mathematics, MDPI, vol. 11(4), pages 1-14, February.
    6. Weam Alharbi & Snezhana Hristova, 2021. "New Series Solution of the Caputo Fractional Ambartsumian Delay Differential Equationation by Mittag-Leffler Functions," Mathematics, MDPI, vol. 9(2), pages 1-18, January.

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